Geodesic
On stability of linear autonomous difference equations with complex coefficients
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 35 (2025) no. 1, pp. 3-26

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We study the stability of linear autonomous scalar difference equations with complex coefficients. For an equation with an arbitrary number of delays, we propose a simple proof of the linear connectivity of the stability region in the space of coefficients. This result allows us to assert that the stability region of the equation in the space of coefficients is the region of the $D$-decomposition of this space containing the origin of coordinates. Further, we consider some equations with two delays and complex coefficients, for which we give detailed analytic and geometric descriptions of the regions of uniform and exponential stability.
Keywords: difference equation, exponential stability, uniform stability
Mots-clés : $D$-decomposition 
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I. A. Aksenenko; K. M. Chudinov. On stability of linear autonomous difference equations with complex coefficients. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 35 (2025) no. 1, pp. 3-26. http://geodesic.mathdoc.fr/item/VUU_2025_35_1_a0/